Mats Cedervall

Combined instrumental variable and subspace fitting approach to parameter estimation of noisy input-output systems

The paper considers the problem of estimating the parameters of linear discrete-time systems from noise-corrupted input-output measurements, under fairly general conditions: the output and input noises may be auto-correlated and they may be cross-correlated as well. By using the instrumental-variable (IV) principle a covariance matrix is obtained, the singular vectors of which bear complete information on the parameters of the system under study. A weighted subspace fitting (WSF) procedure is then employed on the sample singular vectors to derive estimates of the parameters of the system. The combined IV-WSF method proposed in the present paper is noniterative and simple to use. Its large-sample statistical performance is analyzed in detail and the theoretical results so obtained are used to predict the behavior of the method in samples with practical lengths. Several numerical examples are included to show the agreement between the theoretically predicted and the empirically observed performances. >

Efficient maximum likelihood DOA estimation for signals with known waveforms in the presence of multipath

We present a large-sample maximum likelihood (ML) algorithm for estimating the directions of arrival (DOAs) and signal amplitudes of known, possibly coherent signals impinging on an array of sensors. The algorithm is an extension of the DEML method of Li et al., that handles coherent multipath that may be present in the signals. The algorithm is computationally efficient because the nonlinear minimization step decouples into a set of minimizations of smaller dimension.

Detection tests for array processing in unknown correlated noise fields

This paper introduces two eigenvalue-based rules for estimating the number of signals impinging on an array of sensors along with a spatially correlated noise field. The first rule, called S, is derived under the assumption that the noise spatial covariance is block diagonal or banded. The assumption underlying the second detection rule, named T, is that the temporal correlation of the noise has a shorter length than that of the signals. In both cases, a matrix is built from the array output data covariances, the smallest eigenvalue of which is equal to zero under the hypothesis that the source number is overestimated. The sample distribution of the aforementioned smallest eigenvalue is derived and used to formulate the detection rules S and T. Both these rules are computationally quite simple. Additionally, they can be used with a noncalibrated array. The paper includes numerical examples that lend empirical support to the theoretical findings and illustrate the kind of performance that can be achieved by using the S and T detection rules.

System identification from noisy measurements by using instrumental variables and subspace fitting

This paper considers the estimation of the parameters of a linear discrete-time system from noise-perturbed input and output measurements. The conditions imposed on the system are fairly general. In particular, the input and output noises are allowed to be auto-correlated and they may be cross-correlated as well. The proposed method makes use of an instrumental variable (IV)-vector to produce a covariance matrix that is pre- and postmultiplied by some prechosen weights. The singular vectors of the so-obtained matrix possess complete information on the system parameters. A weighted subspace fitting (WSF) method is then applied to the aforementioned singular vectors to consistently estimate the parameters of the system. The IV-WSF technique suggested herein is noniterative and easy to implement, and has a small computational burden. The asymptotic distribution of its estimation errors is derived and the result is used to motivate the choice of the weighting matrix in the WSF step and also to predict the estimation accuracy. Numerical examples are included to illustrate the performance achievable by the method.

Order estimation method for subspace-based system identification

Abstract All subspace-based methods for system parameter estimation require an estimate of the order of the system under study. Most typically, the order estimate is obtained by means of ad-hoc thresholding methods, such as those based on the visual inspection of the eigenvalues (or singular values) of an appropriate data covariance matrix. This paper introduces a statistical rule for testing whether the smallest eigenvalue of the covariance matrix is zero. Then, the paper goes on to propose an order estimation method which builds on the aforementioned rank estimation rule. To illustrate the performance of the proposed subspace-based order estimation methodology, we apply it to the case of ARMA signals.

Decoupled maximum likelihood angle estimation for coherent signals

We present an algorithm for estimating the directions of arrival (DOAs) and signal amplitudes of known, possibly coherent signals impinging on an array of sensors. The algorithm is an extension to the DEML method of Li et al. (see IEEE Transactions on Signal Processing, vol.43, no.9, 1995), used to handle coherent multipath which may be present in the signals. We derive a large-sample maximum likelihood estimator for the signal parameters. The algorithm is computationally efficient because the nonlinear minimization step decouples into a set of minimizations of smaller dimension. We also derive the asymptotic statistical variance of the parameter estimates, develop an analytical expression for the CR bound for this signal scenario, and compare the two both theoretically and numerically.

Mode-type algorithm for estimating damped, undamped, or explosive modes

We propose a new algorithm for estimating the parameters of damped, undamped, or explosive sinusoidal signals. The algorithm resembles the MODE algorithm, which is commonly used for direction of arrival estimation in the array signal processing field. It is derived as a natural approximation to an asymptotically (high-SNR) optimal parameter estimator and has excellent statistical accuracy. Nevertheless, it is computationally simple and easy to implement. Numerical examples are included to illustrate the performance of the proposed method.

An Eigenvalue-Based Detection Test for Array Signal Processing in Unknown Correlated Noise Fields

Abstract This paper introduces an eigenvalue-based rule for detecting the number of signals impinging on an array of sensors along with a spatially correlated noise field. The assumption underlying the detection rule, named T, is that the temporal correlation of the noise has a shorter length than that of the signals. A matrix is built from the array output data covariances, the smallest eigenvalue of which is equal to zero under the hypothesis that the source number is overestimated. The sample distribution of the aforementioned smallest eigenvalue is used to formulate the detection rule T. The rule is computationally quite simple and can be used with a non-calibrated array. The paper includes numerical examples that lend empirical support to the theoretical findings and illustrate the kind of performance that can be achieved by using the T detection rule. The T-rule is also applied to some real hydroacoustic data.

MODE-type algorithm for estimating damped, undamped or explosive modes

We propose a new algorithm for estimating the parameters of damped, undamped or explosive sinusoidal processes. The algorithm resembles the MODE (method of direction estimation) algorithm which is commonly used for direction of arrival estimation in the array signal processing field. The algorithm is asymptotically (for high SNR) optimal. Nevertheless it is computationally simple and easy to implement. Numerical examples are included to illustrate the performance of the proposed method.

On LP-MUSIC

Studies the consistency properties of a method recently proposed for temporal or spatial frequency estimation from noisy data. The method in question is a MUSIC technique that makes use of a linear prediction algorithm to determine the signal subspace. It is shown that the signal subspace determined by the subject linear prediction-MUSIC (LP-MUSIC) algorithm can collapse in certain scenarios and. Hence, that the LP-MUSIC frequency estimates are not always consistent. The difficulties LP-MUSIC may encounter in some cases are illustrated by means of numerical examples. >